There were 2 major sexual revolutions in Russia, both following a revolutionary change in government: One in the 1920's after the creation of the Soviet Union and the second in the 1990's after the fall of the Soviet Union.
The Soviet Union was the result of the Russian Bolshevik revolution of 1917 and eventually "united" together 15 republics (of the former Russian Empire) with the republic called "Russia" being larger than all the other republics combined. The Union of Soviet Socialistic Republics (USSR = Soviet Union) lasted almost 70 years. The Soviet Union and the United States were allies in World War II. Nazi Germany invaded the countries to the east of it and then invaded the Soviet Union. Soviet troops eventually liberated these East European countries from the Nazis and met in Germany with American troops invading Germany from the west in 1945.
But the Soviet occupiers supported the minority pro-socialist sentiments in these East European countries and enabled socialist groups there to take over. The U.S. didn't like this and the so called "cold war" got started, ending only a few years before the collapse of the Soviet Union in 1991. After World War II there were 3 civil wars in which the United States and the Soviet Union supported opposing sides: Korea, Vietnam, and Afghanistan. The Soviet Union claimed to be democratic but it wasn't since only one political party was permitted: the Communist Party, which supported the socialist government. The West called the Soviet Union "communist", while the Soviet union insisted that it was "socialist".
Thus for the decades of the cold war, the Soviet Union and the United States were mortal enemies and the media in both countries was often overly critical of the other. The history of the other country was often distorted. This distortion of history continued even after the cold was ended and the Soviet Union collapsed. The first major studies of sex in the Soviet Union happened only after the Soviet Union ceased to exist (with one minor exception). These studies falsely claimed that the Soviet Government (and the revolution that created it) had tried to suppress sex [Carleton pp. 1-2] when in fact during the 1920's the first sexual revolution in the world had taken place in the Soviet Union.
Today (2017) a majority of people say they liked living the socialist Soviet Union better than they like living in capitalist Russia today (and other ex-Soviet countries). Also it's claimed that women had better sex under socialism but since this claim is based on information from Bulgaria and Germany, it's not necessarily true for the Soviet Union.
Per Russian Wikipedia marriage today between close relatives is prohibited but sex between close relatives is allowed provided the people involved are not under the age of consent (currently 16). Per article 6 incest has been legal in Russia since the start of the Soviet Union in 1922.
Thus it's legal for a parent to have consensual sex with a 16-year-old son or daughter or a 16+ age brother-sister pair to have sex. How often does this happen? It's a topic for which it appears no surveys have been made but there is lot about "incest" on the Russian Internet (runet). If one does a search for "incest" on the Russian internet, the results are mostly porn sites which have videos and pictures of people that are supposedly closely related having sex. There are also some short stories written by people who claim to have had incestuous relationships and tell the world about them (in Russian of course). Some of them go into the details of sexual encounters and thus would be considered pornographic. There are also discussions of the subject by Internet users on the Russian Internet, including people asking if others agree with their thoughts of possibly entering into a sexual affair with a close relative.
One case which is speculated on the Internet to be more common than others (note: sex between cousins is not considered incest) is that of divorced mother and son. The son puts pressure on his mother to have sex with him and the mother, who is lonely and has no boyfriend at the time, gives in and starts having sex with her son.
Besides Russia, incest in Spain and Portugal has been legal since 1978. See Incestuous Spanish father and daughter 'couple' fight to keep baby - Telegraph But in most of the world it's illegal and there are strong traditional taboos against it. In Russia, there are some arguments favoring it on the Internet: One doesn't have to spend a lot of time (and money ??) searching for a suitable sex partner. There is often no travel time involved in meeting up with each other for sex. There may be less chance of getting a sexually transmitted disease.
A major downside to incest with a close relative occurs if the couple has children. The chance that such a child will be born with genetic defects or problems increases by up to "30% over normal (10%-30%). See Consanguinity Fact Sheet -- Debunking Common Myths This means, for example, that if ones baby with a non-relative (normal marriage) has an x% chance of a serious genetic defect, ones baby with a close relative (sibling or parent) has a 1.3x% chance of having such a defect. Thus the danger is not a high as many imagine and for some it may be an acceptable risk. But such a risk obviously doesn't exist at all if the couple doesn't have children.
There is the question of whether or not many people in Soviet Russia even knew that incest was legal. In 1932 when asked about if incest was legal or not, Soviet leader Trotsky (later murdered by Stalin) claimed not to know Trotsky (question 7). Incest just wasn't news since people kept it secret and if the authorities did find out, no one got arrested. Thus it didn't seem to get any publicity in the Soviet Russia. It was legal, not because there existed any law making it legal but because no law existed that prohibited it. One wonders if Stalin realized that it was legal and if so, why he didn't try to outlaw it since under Stalin both homosexuality and abortion became outlawed.
The abundance of incest on the Russian Internet (both porn and more serious articles, discussions, and tales) tends to make it less of a taboo subject in Russia today (2017). Thus there may be more acceptance and practice of incest in Russia today than elsewhere in the world..
Back in the USSR: 64 per cent of Russians say life was better in the Soviet Union than now Life was better in the Soviet Union than afterwards, according to a majority of people who had a clear memory and experience of living under communism in the USSR. By Will Stewart Published (in British newspaper "Express"): Updated: 14:27, Wed, Aug 17, 2016
Why Women Had Better Sex Under Socialism New York Times, Sunday Review Aug. 12, 2017. from "Red Century" by Kristen R. Ghodsee
Baur, Brian James. Other Russias, homosexuality and the crisis of post-Soviet identity. Palgrave McMillan, 2009.
Carleton, Gregory. Sexual Revolution in Bolshevik Russia, University of Pittsburgh Press, 2005.
Kon, Igor. Seksualnal'naia
See Trotsky, Leon: Family Relations Under the Soviets.